Near the speed of light

What happens when we travel near the speed of light?

Let's say you're traveling at 99.5% the speed of light. That's 299792458 meters per second, or 185351 miles per second. You're heading straight towards Proxima Centauri, the nearest star besides the Sun. Proxima Centauri is about 4 light years away, meaning that it takes a beam of light four years to get from here to there. 4 light years is about 2.3 x 10¹³ miles.

Large numbers, eh?

It might seem as if you would get to Proxima Centauri in about 4 years. After all, you're practically like a beam of light yourself now. But things are not so simple when we get close to the speed of light. To continue with our calculations, we will need something known as the Lorentz factor. The Lorentz factor is just some number, symbolized with (the letter gamma).

= 1/sqrt( 1 - (v/c)²)

v is the velocity, and c is the speed of light. In our example, is approximately equal to 10.

One of the things that happens when you travel near the speed of light, is that all distances in the direction of travel get shortened by a factor of . The Earth will seem like a squashed spheroid to you. It will also seem as if Proxima Centauri is not 4 lightyears away, but 0.4 lightyears away. So you will get there in 0.4 years without ever breaking the speed limit set by Relativity!

I would be on Earth, watching you. I would see you arrive at Proxima Centauri 8 years later. From my perspective, it took you 4 years to get there, and 4 more years for your signal to return to me. Let's say that you decided to return home, and sent a message to me saying so. It would take the message 4 years to get to me, and you will appear about one week later, since you travel at nearly the same speed as your own message.

By the time you returned, about 8 years would have passed on Earth. From your perspective, the entire trip only took 0.8 years. From your perspective, Earth has skipped ahead in time by about 7.2 years. From my perspective, it seems like you hardly aged over that long trip.

Let's say that you're about 100 kg (220 lb). Once you start moving near the speed of light, your mass increases by a factor of , so you will appear to be 1000 kg. Since your mass increased by 900 kg, guess how much energy it required to mobilize you? That's right, E=mc². In your case, this will be 8.1 x 10¹⁹ Joules, or about twenty thousand megatons. And that's just you by yourself. If you're in some kind a space ship, the space ship might carry about a million more megatons of energy. You would probably make quite an explosion if you hit one of Proxima Centauri's planets, if it has any. Not that we were planning to do anything like that.

You and your spaceship will appear to be flattened by a factor of . You will seem as flat as a pancake. You will probably look quite absurd, a massive, flying, pancaked person. What's more, your colors would be all shifted. When you're flying away, you will be redshifted by about a factor of 20. Basically, I will only see what little ultraviolet light you emit. But when you're flying towards me, you will be blueshifted by a factor of 20. Much of that infrared light which you normally radiate will now be blueshifted into visible light and x-rays. I'm not sure what color you would appear, but I estimate about the color of a star of 6,000 degrees, like the sun--a yellowish white.

You, while on your journey, will see something even more exciting. Everything behind you will be redshifted by a factor of 20. You would see the extreme ultraviolet range. In the ultraviolet range, most stars will seem much dimmer, except for the hotter ones, including white dwarfs. If you look in front of you, light is blueshifted by a factor of 20, so you will see part of the middle infrared spectrum. You can see giant dust clouds and nebula in this range. Some of these dust clouds are where stars will form. And as you swing your head around, looking from front to back, you will see all the ranges between middle infrared and extreme ultraviolet. I'm sure it would be quite an experience.

Falsifiability and having it both ways

Long time readers might have figured out that I have it in for Karl Popper's philosophy of falsifiability. I don't believe Popper gave an accurate description of how science works, nor how science should work. I think Popper's philosophy is at best a clunkier version of induction, and at worst, simply wrong. It is also prone to abuse and/or misunderstanding.

However, I will say that there is more than just a grain of truth to it. At the heart of the philosophy of falsifiability is the recognition a particular logical fallacy. I am not sure if this fallacy has a common name, but I will call it "having it both ways".

Take the following illustrative real-life example (via Phil Plait). Patricia Putt, a claimed psychic applied for the James Randi's Million Dollar Paranormal Challenge. In this challenge, Putt and the testers agreed on an experiment which would be able to test her ability to "read" people. In the experiment, Putt read ten women and wrote down descriptions of each of them. Each of the women was asked to choose the description out of the ten which fit her best. If five of the women picked out the correct description, Putt would move on to the final testing.

As it happened, none of the women picked out the correct description. At a later time, Putt decided that this meant she had actually gotten 10 out of 10, since each of the women had picked out one of her descriptions. Nevermind that each of the women were asked to pick out a description, and that none of them picked out the correct one.

There are only two possible results to this experiment:
(1) Most of the women pick the correct description.
(2) Few or none of the women pick the correct description.

If (1) had occurred, then that would be evidence in favor of Putt's psychic abilities. Not absolute evidence, mind you, since it could also happen by chance. But it would be evidence enough that we would want to investigate it further. However, what actually occurred was (2); none of the women chose correctly. Putt claims that this is nonetheless evidence in favor of her psychic abilities. But she can't have it both ways! We might say that one possible result is evidence for psychic ability, or that another possible result is evidence for psychic ability, but we cannot say that all possible results would be evidence for psychic ability.

If all possible results of an experiment have the same conclusion, then there would hardly be any need to perform the experiment in the first place. Even before the experiment occurs, we know that either (1) or (2) will occur. According to Putt, either way, this means the experiment comes out in her favor. But then, what is the point of the experiment? Can we really call it experimental evidence if we think it is unnecessary to ever actually perform the experiment?

The bottom line is that if you want to entertain the possibility of evidence for something, you must also entertain the possibility of evidence against it. You can't have one without the other.

I propose that this fallacy doesn't just make for bad science, it makes for bad reasoning, period.